A point P divides the line segment joining the points A 3- -5 and B -4- 8 such that AP-PB-k-1- If P lies on the line x - y - 0- then find the value of k-

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Section Formula

A point P div...

Question

A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that $\frac{A P}{P B} = \frac{k}{1} .$ If P lies on the line x + y = 0, then find the value of k.

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Solution

given the line AB is divided in the ratio K:1

applying section formula
$x equals fraction numerator k asterisk times left parenthesis negative 4 right parenthesis plus 1 asterisk times 3 over denominator k plus 1 end fraction equals fraction numerator 3 minus 4 k over denominator k plus 1 end fraction a l s o space y equals fraction numerator k asterisk times 8 plus 1 asterisk times left parenthesis negative 5 right parenthesis over denominator k plus 1 end fraction equals fraction numerator 8 k minus 5 over denominator K plus 1 end fraction sin c e space p left parenthesis x comma y right parenthesis space s a t i s f i e s space t h e space l i n e space x plus y equals 0 p u t t i n g space v a l u e s space o f space x space a n d space y fraction numerator 3 minus 4 k over denominator k plus 1 end fraction plus fraction numerator 8 k minus 5 over denominator K plus 1 end fraction equals 0 fraction numerator 3 minus 5 minus 4 k plus 8 k over denominator k plus 1 end fraction equals 0 minus 2 plus 4 k equals 0 4 k equals 2 k equals 1 half$

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Similar questions

A point P divides the line segment joining the points $A (3, - 5)$ and $B (- 4, 8)$ such that $\frac{A P}{B P} = \frac{K}{1}$ . If P lies on the line $x + y = 0,$ then fine the value of K.

Q. A point P divides the line segment joining the points A(3, −5) and B(−4, 8) such that

\frac{AP}{PB} = \frac{k}{1} .

If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]

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. If P lies on the line x+y=0 ,then find the value of k

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A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that APPB=k1. If P lies on the line x + y = 0, then find the value of k.

given the line AB is divided in the ratio K:1 applying section formula

A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that $\frac{A P}{P B} = \frac{k}{1} .$ If P lies on the line x + y = 0, then find the value of k.